Sam has 8 more 10-cent coins than 5-cent coins. After he used 17 of his 10-cent coins, the total value of 10-cent coins is $2.90 more than the total value of 5-cent coins. How many coins did he have at first?
| |
10¢ |
5¢ |
| Before |
1 u + 8 |
1 u |
| Change |
- 17 |
|
| After |
1 u - 9 |
1 u |
| |
10¢ |
5¢ |
| Number |
1 u - 9 |
1 u |
| Value |
10 |
5 |
| Total value |
10 u - 90 |
5 u |
$1 = 100¢
$2.90 = 290¢
Number of 10¢ coins in the end
= 1 u + 8 - 17
= 1 u - 9
Total value of 10¢ coins in the end
= 10 x (1 u - 9)
= 10 u - 90
Total value of 5¢ coins in the end
= 5 x 1 u
= 5 u
After using 17 10-cent coins, the value of 10-cent coins is 290¢ more than the value of 5-cent coins. If another 290¢ is added to the 5-cent coins, the total value of 10-cent coins and 5-cent coins will be the same.
10 u - 90 = 5 u + 290
10 u - 5 u = 290 + 90
5 u = 380
1 u = 380 ÷ 5 = 76
Number of coins that Sam had at first
= 1 u + 1 u + 8
= 2 u + 8
= (2 x 76) + 8
= 152 + 8
= 160
Answer(s): 160
